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State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill & Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). But do SSMs truly have an advantage (over transformers) in expressive power for state tracking? Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class 𝖳𝖢0. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state" in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems. 

Abstract Language models are typically evaluated on their success at predicting the distribution of specific words in specific contexts. Yet linguistic knowledge also encodes relationships between contexts, allowing inferences between word distributions. We investigate the degree to which pre-trained transformer-based large language models (LLMs) represent such relationships, focusing on the domain of argument structure. We find that LLMs perform well in generalizing the distribution of a novel noun argument between related contexts that were seen during pre-training (e.g., the active object and passive subject of the verb spray), succeeding by making use of the semantically organized structure of the embedding space for word embeddings. However, LLMs fail at generalizations between related contexts that have not been observed during pre-training, but which instantiate more abstract, but well-attested structural generalizations (e.g., between the active object and passive subject of an arbitrary verb). Instead, in this case, LLMs show a bias to generalize based on linear order. This finding points to a limitation with current models and points to a reason for which their training is data-intensive.1 

Naturally-occurring information-seeking questions often contain questionable assumptions -- assumptions that are false or unverifiable. Questions containing questionable assumptions are challenging because they require a distinct answer strategy that deviates from typical answers to information-seeking questions. For instance, the question "When did Marie Curie discover Uranium?" cannot be answered as a typical when question without addressing the false assumption "Marie Curie discovered Uranium". In this work, we propose (QA)2 (Question Answering with Questionable Assumptions), an open-domain evaluation dataset consisting of naturally-occurring search engine queries that may or may not contain questionable assumptions. To be successful on (QA)2, systems must be able to detect questionable assumptions and also be able to produce adequate responses for both typical information-seeking questions and ones with questionable assumptions. We find that current models do struggle with handling questionable assumptions -- the best performing model achieves 59% human rater acceptability on abstractive QA with (QA)2 questions, leaving substantial headroom for progress.